There are two firms producing identical seltzer water, each with a constant marginal cost of 3 with no other associated costs. Let the market demand for seltzer water be given by Q = 168 − 4 min{p1, p2}, where Q = q1 + q2 is the total market quantity (number of cases) and p1 is firm 1’s price and p2 is firm 2’s price. Suppose that the firms split the market evenly when p1 = p2. (a) Suppose the firms act as Bertrand (price) competitors. (i) What is the equilibrium price set by each firm? (ii) What is the equilibrium quantity sold by each firm? (iii) What are the equilibrium profits for each firm? (b) Suppose that, prior to competing in prices, the firms can choose their capacities. They do so simultaneously and independently, but know each other’s capacity prior to competing in prices. (i) What capacity should each firm invest in if they wanted to maximize joint profits? Why do these capacities not constitute a Nash equilibrium? (ii) What capacities would each firm choose in the Nash equilibrium? What is prevailing market output, market price, and each firm’s profits in this equilibrium?